The matrix A = [ array ccc 1 & 3 & 2 1 & x-1 & 1 2 & 7 & x-3 array ] will have inverse for every real number x except for

Step-by-step solution

A= [ array ccc 1 & 3 & 2 1 & x-1 & 1 2 & 7 & x-3 array ] aligned & |A|=1[(x-1)(x-3)-7]-3[(x-3)-2]+2[7-2(x-1)] & =x^2-11 x+29 aligned If inverse will not exist then | A |=0 aligned & x ^2-11 x +29=0 & x = 11 5 2 aligned